In this renewal application, the focus will be on the development of robust single particle cryo-EM analysis methods that incorporate, from their inception, statistical verification of the results. We will concentrate on three specific areas: (1) 2-D image alignment, (2) ab initio structure determination, and (3) quantitative description of macromolecular conformational variability based on data resampling methodology. In (1), a novel 2-D image alignment approach based on the Maximum Likelihood (ML) paradigm will make use of an Expectation Maximization algorithm and incorporate a precise image formation model. The feasibility of the method requires excellent computational efficiency, which will be achieved by spanning the angular parameters in the likelihood function over a finite set, in agreement with properties of typical EM data. We will be able to optimize performance of the proposed method by using filtration in the Fourier Harmonics basis to model alignment-induced blurring of the image data. We also propose to use the eigenanalysis of the alignment parameter covariance matrix obtained from ML to classify images directly from alignment information. In (2), we will greatly improve the performance and reliability of previously developed common lines-based methodology by introducing additional discrepancy terms that follow from considering 2-D overlap between intersecting Fourier planes. In combination with improved alignment algorithms, this methodology will result in a robust approach for generation of initial cryo-EM structures that will overcome current limitations due to low Signal-to-Noise Ratio and structural heterogeneity of the data. In (3), a novel data resampling approach designed to overcome limitations arising from the strongly anisotropic distribution of projections in cryo-EM data sets will permit automation of variance and covariance estimation for 3-D reconstructions. Eigenanalysis of large volume sets generated through data resampling will be used to calculate (directly from the image data) eigenvectors describing the conformational modes of a macromolecular assembly. Structures calculated from data subsets identified through this eigenvector analysis will provide higher-resolution models of conformations relevant for studies of molecular function. Rather than incremental improvements, the methods we propose to develop represent novel approaches that address specific issues currently hindering further development of single particle cryo-EM. To assure maximum portability and efficient dissemination, these new methods will be implemented within the currently deployed SPARX image processing package. PUBLIC HEALTH RELEVANCE: High-resolution cryo-electron microscopy (cryo-EM) has become an important tool for the structure/function determination of large macromolecular complexes. Even at subnanometer resolution cryo-EM maps provide a wealth of structural information, eventually leading to determination of the secondary structure, as demonstrated by our work on the structure of the ribosome. In addition, cryo-EM is a unique structural technique in its ability to detect conformational variability of large molecular assemblies within one sample that may contain a mixture of complexes in various conformational states. We propose development of dedicated data processing and statistical tools for establishing the number of conformers in the data set, and for studies of conformational modes of the structure, as directly obtained from the EM data.